What is the LCD in its factored form of the following rational expression subtraction?
x2+2xx2+7x−8−xx−1
(1 point)
Responses
(x−1)2(x+8)
left parenthesis x minus 1 right parenthesis squared left parenthesis x plus 8 right parenthesis
x(x+2)
x left parenthesis x plus 2 right parenthesis
(x−1)(x2+7x−8)
left parenthesis x minus 1 right parenthesis left parenthesis x squared plus 7 x minus 8 right parenthesis
(x−1)(x+8)
left parenthesis x minus 1 right parenthesis left parenthesis x plus 8 right parenthesis
To find the least common denominator (LCD) in its factored form of the given rational expression subtraction, we need to factor each of the denominators and then find their common factors.
The denominators are:
1) x - 1
2) x^2 + 7x - 8
1) Factoring x - 1:
x - 1 is already in its factored form.
2) Factoring x^2 + 7x - 8:
We need to find two numbers that multiply to -8 and add up to 7.
The numbers are 8 and -1, because 8 * -1 = -8 and 8 + (-1) = 7.
So, x^2 + 7x - 8 can be factored as (x + 8)(x - 1).
The LCD in its factored form is the product of the distinct factors:
LCD = (x - 1)(x + 8)
So, the correct answer is:
(x - 1)(x + 8)
To find the LCD (Least Common Denominator) in the factored form of the given rational expression subtraction, you need to identify the common factors between the denominators.
The denominators of the rational expression subtraction are (x - 1) and (x + 8).
To find the Least Common Denominator, you need to factor the denominators into their prime factors.
Factorizing (x - 1):
(x - 1) can't be further factored, as it is already in its simplest form.
Factorizing (x + 8):
(x + 8) can't be further factored, as it is already in its simplest form.
Now, you have the factored form of the denominators:
(x - 1) and (x + 8)
Since there are no common factors between the denominators, the LCD of the rational expression subtraction is the product of the denominators:
LCD = (x - 1)(x + 8)
Therefore, the correct option is: (x - 1)(x + 8).